Dispersion of Gravitational Waves by a Collisionless Gas

Gravitational waves in a hot collisionless gas do not propagate on null geodesics. Using the methods of plasma kinetic theory, we derive dispersion relations from a self-consistent, first-order perturbation expansion of Einstein's, Boltzmann's, and the geodesic "force" equations. The wave's interaction with the higher shear moments of the ensemble introduces new length scales into the dispersion relations, which can affect the familiar modes and allow new ones. For an isotropic photon gas, the strongest mode has the dispersion relation ω²≈c²k²-144πGP5c², where P is the gas pressure. Because the length scale c²(GP)1/2 is very large (10³⁰ cm for the 3 ^∘{}K cosmic radiation), this retarded wave is practically indistinguishable from the vacuum solution. We also find some weak, novel effects, like collisionless amplification and evanescent wave modes, which are very sensitive to the particles' momentum distribution.